Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
n = int(raw_input())

yes = 0
N = 100005
for k in range(1, N):
	target = n - (k*(k+1)/2)
	if (target < 0): break
	l = 1
	r = N
	ans = -1
	while (l <= r):
		mid = (l+r)/2
		cur = mid*(mid+1)/2
		if (cur == target):
			ans = mid
			break
		elif (cur < target):
			l = mid+1
		else:
			r = mid-1
	if (ans != -1):
		yes = 1
		break

if (yes):
	print "YES"
else:
	print "NO"